Question

Question 1 The hyperbolic cosine cosh(x) is the average of eand e-". That is, cosh(3) et te I 2. It is useful for describing a chain or wire supported at its ends. Electrical wire strung between two towers forms a curve called a catenary modeled by the equation y = 10 cosh (10) Find the length of the suspended wire.

Answer 1

Solution 1: We have ex +e- cosh(x) 2 x y = 10 cosh (1) e 10 + e 10 2 х х х = y = 5e10 + 5e 10 dy 1 = 5e10 x + 5e 10 x dx 10 dy 1 х e 10 dx (-1) 10 2 1 ::1+ dx, =1+á leio (eið – e75) c)-1+31(et) +(67) * - 2 x eko x ej) 1+ 1+ 4 62 - 4+ (eñi) + (czó) - 2 * (vá)? +(017) +2x eťo xei 1+ 4

-x, 2 e 10 + e 10 1+ c) ? (eið +evő)? 4 The arc length of “y" over x € (-10,10) is 10 2 e 10 + e 10 LE s 1+ dx = -dx dx 4 -10 -10 10 LE je** tet dx=(1008– 10 10e 10 -10 -10 1 L 5(10(e? – e-1) – 10(e-1 – e-)) L = 5(2e1 – 2e-1) L=5(e-) Answer

Solution 2: Given the radius of ball is 17 units. Volume of Ball 4 Vi z tr3 4 22 = 3*7*(17)3 = 2.05878 x 104 Drilled shape is approximate cylinder with radius 3 and height 33 units. Volume of Cylinder V2 = arah 22 X 9 X 33 7 = 0.93342 x 104 =- Volume of resulting Solid V3 = V1 – 12 V3 = 2.05878 x 104 – 0.93342 x 104 V3 = 1. 12536 x 104 cubic units